Question

pooja and ritu can do a piece of work in 17 1/7 days. if one day work of Pooja be three fourth of one day work of ritu; find in how many days each will do the work alone.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Pooja and ritu can do a piece of work in $\rm 17 \dfrac { 1 } { 7 }$ days.

• One day work of pooja is three fourth of one day work of ritu.

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$\red{\underline \bold{To \: Find:}}$

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• Days each will require to do the work alone.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let pooja can do the work alone in 'x' days

Let ritu can do the work alone in 'y' days

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$\underline{\bold{\texttt{One day work of pooja:}}}$

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$\purple\longrightarrow$ $\sf \dfrac { 1 } { x }$

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$\underline{\bold{\texttt{One day work of ritu:}}}$

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$\purple\longrightarrow$ $\sf \dfrac { 1 } { y }$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\sf \longmapsto \dfrac { 1 } { x } + \dfrac { 1 } { y } = \dfrac { 7 } { 120 }$ ----------(1)

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Also,

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$\sf \longmapsto \dfrac { 1 } { x } = \dfrac { 3 } {4 } \times \dfrac { 1 } { y }$

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$\sf \longmapsto \dfrac { 1 } { x } = \dfrac { 3} { 4y}$

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$\sf \longmapsto 4y = 3x$

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$\sf \longmapsto x = \dfrac { 4y } { 3 }$ -----(2)

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$\underline{\bold{\tt{Putting \: x \: =\: \dfrac { 4y } { 3 }\: in \: equation \: (1) }}}$

$\:\:$

$\sf \longmapsto \dfrac { 1 } { \dfrac { 4y } { 3 } } + \dfrac { 1 } { y } = \dfrac { 7 } { 120 }$

$\:\:$

$\sf \longmapsto \dfrac { 3 } { 4y } + \dfrac { 1 } { y } = \dfrac { 7 } { 120 }$

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$\sf \longmapsto \dfrac { 3 + 4 } { 4y } = \dfrac { 7 } { 120 }$

$\:\:$

$\sf \longmapsto \dfrac { 7 } { y } = \dfrac { 7 } { 30 }$

$\:\:$

$\sf \longmapsto y = 30$

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$\underline{\bold{\texttt{Putting y = 30 in equation (2)}}}$

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$\sf \longmapsto x = \dfrac { 4(30)} { 3 }$

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$\sf \longmapsto x = \dfrac { 120} { 3 }$

$\:\:$

$\sf \longmapsto x = 40$

$\:\:$

Hence Pooja will take 40 days to do the work alone.

Ritu will take 30 days to do the work alone.

$\rule{200}5$

Answer 2

Answer:

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Step-by-step explanation:

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